$1.$ The $\_\_\_\_\_\_$ model is used to estimate the $\_\_\_\_\_\_$ fraction in two$-$phase flow systems.

$2.$ In mini channels, the drift flux model must be modified due to the $\_\_\_\_\_\_\_$ effect, impacting the $\_\_\_\_\_\_\_$ velocity.

$3.$ Three$-$phase flow involves the interaction of gas, $\_\_\_\_\_\_\_,$ and $\_\_\_\_\_\_\_$ phases, complicating flow analysis.

$4.$ Agitated vessels enhance $\_\_\_\_\_\_\_$ transfer and mixing in gas$-$solid$-$liquid systems by creating a $\_\_\_\_\_\_\_$ environment.